integral from 0 to 1 of sqrt(1+cos(pix))

Lösung

\int_{0}^{1} 1 + cos (π x) d x

\frac{2 2}{π}

Dezimale

0.90031 \dots

Schritte zur Lösung

\int_{0}^{1} 1 + cos (π x) d x

Berechne das unbestimmte Integral:

\int 1 + cos (π x) d x = \frac{2 2}{π} sin (\frac{π x}{2}) + C

Berechne die Grenzen:

\int_{0}^{1} 1 + cos (π x) d x = \frac{2 2}{π} - 0

= \frac{2 2}{π} - 0

Vereinfache

= \frac{2 2}{π}

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